where the parameters \(k,a,\)  are general complex numbers and \(Re(u)<Re(m)<1/2, Re(m)<Re(v)\) . This definite integral will be used to derive special cases in terms of special functions and fundamental constants. The derivations follow the method used by us in [1]}. This method involves using a form of the generalized Cauchy's integral formula given by
\(\frac{y^k}{\Gamma (k+1)}=\frac{1}{2\pi i}\int _{C}\frac{e^{wy}}{w^{k+1}}dw.\) 
